Intro to Springs

Concept:

25m

Intro to Springs Additional Practice Problems

A small block of mass m is on a frictionless table and is attached to a horizontal spring. The spring has stiffness ks and a relaxed length L. The other end of the spring is fastened to a fixed point at the center of the table. The block slides on the table in a circular path of radius R > L. How long does it take for the block to go around once?

1. T = √ 3π2mL2 / ksR2

2. T = √ 4πmR / ksL

3. T = √ 4π2mR2 / ksL

4. T = √ 4πmR / ks (R − L)

5. T = √ 4π2mR2 / ks(R −​ L)2

6. T = √ 2πmR / ks(R −​ L)

7. T = √ 3π2mR2 / ks(R −​ L)

8. T = √ 4π2mR / ks(R −​ L)

9. T = √ 4πmR / ks(L −​ R)

10. T = √ 4π2mR / ks(L −​ R)

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A 3 kg mass slides without friction along the ground at 12 m/s. If the mass contacts a spring, with a force constant of 100 N/m, compresses the spring to a maximum extent, and is then propeled in the opposite direction, how long is the mass in contact with the spring for?

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A vertical spring supports a 5 kg mass at equilibrium by stretching 3 cm. How far would the same spring have to stretch to support a 7 kg mass at equilibrium?

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A mass-spring system has a period on Earth of 1.7 s. On the moon, where gravity is about one-sixth that of the Earth, what is the period of the spring? 

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A simple design for a bathroom scale is to place a platform to stand on atop a spring. If you want the scale to be able to measure weights up to 1500 N, and the scale needs to be 3 cm tall, what is the minimum spring constant required for the scale to work?

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